I would be very grateful for your help. I have 534 observations, 33 indicators (4 point Likert scale), and want to test a 2-factor model. I consider the variables as categorical

***Q1: is this correct?

Then I used modindices (used defaut minimum value=10) where 5 BY statements where suggested, so I allowed 5 indicators to belong to both latent variables as suggested. Results were as follows: Chi-Square(102) value 237.378, highly sign. CFI=0.949,TLI=0.971, RMSE=.050, WRMR=1.12 In model results, two of the variables I allowed to belong to both factors, have a negative Est/S.E. value

***Q2: is this a problem and if so how could I correct it?

There are no modification indices above the minimum value.

***Q3: Any suggestions about strategies to use in order to improve the model (especially in relation to WRMR index)

I am a novice here, but i hope the above makes sense. Thank you very much

Thank you very much for your prompt reply Dr Muthen. Indeed I started with an efa, used the geomin rotated loadings (and theory) to match variables with factors,and tested then with cfa, which does not indicate a great fit. MODINDICES (BY statements) suggested that some variables load on both factors. Would it be appropriate to allow these variables belong to both factors? Or should I delete them? Or? ... I enormously appreciate your guidance and apologies for the very basic questions. with many thanks Ioanna

You can certainly allow variables to load on more than one factor if that makes substantive sense. CFA does not require all variables to load on only one factor. These matters are covered in our "Topic 1" short course, a video of which you can watch for free on the web - see our home page.